Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture
Ronghui Ji
IUPUI, Indianapolis, INCrichton Ogle
OSU, Columbus, OHBobby W. Ramsey
IUPUI, Indianapolis, IN

Abstract
By deploying dense subalgebras of ℓ1(G) we generalize the Bass conjecture in terms of Connes’ cyclic homology theory. In particular, we propose a stronger version of the ℓ1-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy bound property and nilpotent periodicity property, satisfy the ℓ1-Stronger-Bass Conjecture. Moreover, we determine the conjugacy bound for relatively hyperbolic groups and compute the cyclic cohomology of the ℓ1-algebra of any discrete group.
Cite this article
Ronghui Ji, Crichton Ogle, Bobby W. Ramsey, Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture. J. Noncommut. Geom. 4 (2010), no. 1, pp. 83–124
DOI 10.4171/JNCG/50